An Amorphous Phase Precedes Crystallization: Unraveling the Colloidal Synthesis of Zirconium Oxide Nanocrystals

One can nowadays readily generate monodisperse colloidal nanocrystals, but the underlying mechanism of nucleation and growth is still a matter of intense debate. Here, we combine X-ray pair distribution function (PDF) analysis, small-angle X-ray scattering (SAXS), nuclear magnetic resonance (NMR), and transmission electron microscopy (TEM) to investigate the nucleation and growth of zirconia nanocrystals from zirconium chloride and zirconium isopropoxide at 340 °C, in the presence of surfactant (tri-n-octylphosphine oxide). Through E1 elimination, precursor conversion leads to the formation of small amorphous particles (less than 2 nm in diameter). Over the course of the reaction, the total particle concentration decreases while the concentration of nanocrystals stays constant after a sudden increase (nucleation). Kinetic modeling suggests that amorphous particles nucleate into nanocrystals through a second order process and they are also the source of nanocrystal growth. There is no evidence for a soluble monomer. The nonclassical nucleation is related to a precursor decomposition rate that is an order of magnitude higher than the observed crystallization rate. Using different zirconium precursors (e.g., ZrBr4 or Zr(OtBu)4), we can tune the precursor decomposition rate and thus control the nanocrystal size. We expect these findings to help researchers in the further development of colloidal syntheses.


SAXS data fitting
The normalized SAXS patterns are used to determine the particle size and concentration by fitting the experimental intensity. As mentioned in the manuscript, we use as a fitting function the sum of the scattering cross section of a distribution of polydisperse spheres and the experimental signal obtained at 300 • C for the ZrCl 4 reaction mixture multiplied by a fitting parameters (F) set between 0 and 1: The theoretical scattering cross section of distribution of spheres of homogeneous electron density dispersed in a solvent is given by: where n is the particle concentration, ∆ρ is the difference in scattering length density between the particles and the solvent (the contrast), V(R) is the volume of a sphere of radius R, D(R) is the radius distribution, and P(q,R) is the form factor of a sphere. Here, we use a Schultz distribution with Z is related to the polydispersity of the distribution as the polydispersity The fit function can be written as with 4 fitting parameters (R, Z, n and F). In order to provide an estimation of the error S-2 bars for the desired parameters (R and n), we performed fits with a fixed value of Z. For each SAXS pattern, Z was varied using increments of 1 from 1 to 500 and we evaluated the quality of the fit using χ 2 within this Z range ( Figure S1a). We measure the χ 2 value for which the fit is minimal (χ 2 min ) and extract the two Z values which correspond to an increase of χ 2 by 10 %: χ 2 = χ 2 min * 1.1. We then use these two Z values, Z − and Z + , to extract the corresponding R min and R max , n min and n max , which serve as the limits of the error-bars (Figure S1b-c). Figure S1: Determination of the error-bar in SAXS data. (a) Example, for one sample, of the estimation of the quality of the fit, using χ 2 , when varying the parameter Z, Z − and Z + correspond to Z when χ 2 is 10 % larger than its minimum. Variation of the radius (b) and concentration (c) given by the fit when Z is varied.
To account for the intensity of the SAXS signal resulting from the precursors (I precursors ), we used in our fits the experimental signal of the ZrCl 4 reaction at 300 • C (F * I experimental ZrCl 4 at 300 o C ), even for the ZrBr 4 reaction, which may be surprising. First, all the fits were also performed using the SAXS signals of the respective precursors measured at room temperature. Although the fits were visually not as good, the final results were very similar ( Figure S2).
Second, for the ZrCl 4 synthesis at 300 • C, NMR shows that there is no conversion of the precursors at this stage, confirming this signal can be appropriately used in the fitting. However, this was not the case for the ZrBr 4 synthesis which has a faster kinetics, explaining why the ZrBr 4 reaction at 300 • C could not be used in the fitting.
The synthesis yield is calculated by dividing the volume of synthesized particles at a given S-3 point by the total volume of particles possibly synthesized (estimated from the quantities of chemicals used). The estimation of the yield by SAXS is obtained by multiplying the number of synthesized particles by the average particle volume < V > with: and with f(R) given by the Schultz distribution: S1 Here, Z is related to the width of the distribution and < R > the mean sphere radius, both determined by the fits. Figure S2: Effect of the precursor signal used in the fitting of the ex situ SAXS measurements. Comparison of the time evolution of the particle size, concentration, and polydispersity for the (a) ZrCl 4 : Zr(OiPr) 4 · iPrOH and (b) ZrBr 4 : Zr(OiPr) 4 · iPrOH syntheses. The yellow lines were obtained using in the fits the signal of the corresponding precursors measured at room temperature. The dark lines were obtained using the signal from the ZrCl 4 reaction at 300 • C.
S-4 PDF and NMR analysis Figure S3: 31 P NMR spectra in C 6 D 6 for reaction aliquot after 2 hours for 1:1 mixture of ZrBr 4 : Zr(OiPr) 4 · iPrOH showing the formation of ZrBr 4 + n TOPO complex as a byproduct. The NMR shift for the complexes is independently verified by mixing ZrBr 4 with different equivalents of TOPO. While two TOPO equivalents seem to cleanly yield the expected ZrBr 4 · 2 TOPO complex, higher TOPO equivalents result in an unknown complex.
S-9 Figure S9: Extraction of the PDF of amorphous phase after 15 (a), 30 (b), and 60 (c) minutes for ZrCl 4 : Zr(OiPr) 4 · iPrOH reaction. Figure S10: Changes in the contribution of amorphous intermediates captured in situ after 9, 15, and 30 minutes of ZrCl 4 : Zr(OiPr) 4 · iPrOH reaction. Each data point is normalized with reaction crude product (data point after 90 minutes) by scaling the peak intensity at 6.3 A. The difference in the PDFs narrows with time, indicating the disappearance of amorphous intermediate. Unlike the ex situ data, the complete extraction of the amorphous PDF is not possible due to the unavailability of the experimental PDF of ZrCl 4 · 2 TOPO under similar conditions. Figure S11: 1 H NMR spectra of the reaction ZrCl 4 : Zr(OiPr) 4 · iPrOH in C 6 D 6 . Aliquots were taken at different temperatures during the ramp and at different times at the final reaction temperature of 340°C. The bound (α') and unbound (α) propoxide groups are indicated. The integral of α' was used for quantification. Figure S12: 1 H NMR spectra of the reaction ZrBr 4 : Zr(OiPr) 4 · iPrOH in C 6 D 6 . Aliquots were taken at different temperatures during the ramp and at different times at the final reaction temperature of 340°C. The bound (α') and unbound (α) propoxide groups are indicated. The integral of α' was used for quantification.

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Figure S13: Calculation of area under the Bragg peak by subtracting the background (blue) from the reciprocal data (red). The Miller indices corresponding to the Bragg peak are indicated considering the crystal structure is tetragonal zirconia. Table S1: Refined parameters after fitting aliquots from 1:1 reaction mixture of ZrCl 4 : Zr(OiPr) 4 · iPrOH.

Mechanism fitting
This experimental data in Fig. 4b-c was used for fitting in COPASI 4.35. S2 When preparing the data for the program, an x-shift of 0.7 min was given for ZrCl 4 and 1 min for ZrBr 4 to take the ramping into consideration. One cannot start at time = 0 with a precursor conversion that has already progressed by 80 %.

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Reaction with ZrCl 4 Figure S14: Fitting for ZrCl 4 : Zr(OiPr) 4 · iPrOH reaction data with mechanism 3. The root mean square (RMS) value for the fit is 0.00498. Figure S15: Fitting for ZrCl 4 : Zr(OiPr) 4 · iPrOH reaction data with mechanism 3 with second-order kinetics in step 1. The root mean square (RMS) value for the fit is 0.01076. Figure S16: Fitting for ZrCl 4 : Zr(OiPr) 4 · iPrOH reaction data with mechanism 3 with second-order kinetics in step 2. The root mean square (RMS) value for the fit is 0.00374. Figure S17: Fitting for ZrCl 4 : Zr(OiPr) 4 · iPrOH reaction data with mechanism 3 with reversible kinetics in step 1. The root mean square (RMS) value for the fit is 0.00492. Figure S18: Fitting for ZrCl 4 : Zr(OiPr) 4 · iPrOH reaction data with mechanism 4 with first-order kinetics in step 2. The root mean square (RMS) value for the fit is 0.00498. Figure S21: Fitting for ZrBr 4 : Zr(OiPr) 4 · iPrOH reaction data with mechanism 3 with second-order kinetics in step 1. The root mean square (RMS) value for the fit is 0.00171. Figure S22: Fitting for ZrBr 4 : Zr(OiPr) 4 · iPrOH reaction data with mechanism 3 with second-order kinetics in both steps. The root mean square (RMS) value for the fit is 0.00315. Figure S23: Fitting for ZrBr 4 : Zr(OiPr) 4 · iPrOH reaction data with mechanism 3 with reversible kinetics in step 1. The root mean square (RMS) value for the fit is 0.00150. Figure S24: Fitting for ZrBr 4 : Zr(OiPr) 4 · iPrOH reaction data with mechanism 5 with first-order kinetics in step 1. The root mean square (RMS) value for the fit is 0.00137.